Tuesday, October 13, 2015

What Do We Know About Long and Variable Lags?

Purveyors of standard monetary policy lore argue that the effects of monetary policy are subject to "long and variable" lags. The idea appears to originate with Milton Friedman. Quoting from "A Program for Monetary Stability:"

There is much evidence that monetary changes have their effect only after a considerable lag and over a long period and that the lag is rather variable. In the National Bureau study on which I have been collaborating with Mrs. Schwartz, we have found that, on the average of 18 cycles, peaks in the rate of change in the stock of money tend to precede peaks in general business by about 16 months and troughs in the rate of change in the stock of money to precede troughs in general business by about 12 months ... . For individual cycles, the recorded lead has varied between 6 and 29 months at peaks and between 4 and 22 months at troughs.

The "National Bureau study" he mentions, which was not yet published when he wrote "A Program for Monetary Stability," is Friedman and Schwartz's "A Monetary History of the United States, 1867-1960." The Monetary History is the key empirical work backing up Friedman's monetarist ideas. Roughly, this empirical work consisted of a compilation (and construction where necessary) of monetary measurements for the United States over a long period of time, followed by the use of relatively crude statistical methods (crude in the sense that Chris Sims wouldn't get excited by the methods) to uncover regularities in the relationship between money and real economic activity.

As you can see from the quote, turning points in time series were important for Friedman. In part, he wanted to infer causality from the time series - if turning points in the money supply tended to precede turning points in aggregate economic activity, then he thought this permitted him to argue that fluctuations in money were causing fluctuations in output. But, Friedman could not find any regularity in the timing of the effects of money on output, other than that these effects took a long time to manifest themselves. Thus, the notion that monetary policy lags were long and variable.

The Monetary History formed a foundation for Friedman's monetary policy prescriptions. According to Friedman, central banks had two choices. They could either take the car and drive by looking in the rear-view mirror, or take the train. That is, the central bank could exercise discretion, put itself at the mercy of long and variable lags, and perhaps make the economy less stable in the process, or it could simply adhere to a fixed policy rule. From Friedman's point of view, the best policy rule was one which caused some monetary aggregate to grow at a fixed rate forever. If the primary source of instability in real GDP is instability in the money supply, then surely removing that instability would be beneficial, according to Friedman.

The modern version of the Monetary History approach is VAR (vector autoregression) analysis. This preliminary version of Valerie Ramey's chapter for the second Handbook of Monetary Economics is a nice survey of how VAR practitioners do their work. The VAR approach has been used for a long time to study the role of monetary factors in economic activity. If we take the VAR people at their word, the approach can be used to identify a monetary policy shock and trace its dynamic effects on macroeconomic variables - letting the data speak for itself, as it were. Ramey's paper describes a range of results, but the gist of it is that the full effects of a monetary policy shock are not manifested until about 16 to 24 months have passed. This is certainly in the ballpark of Friedman's estimates, though the typical lag (depending on the VAR) is somewhat longer than what Friedman thought. Thus, modern time series analysis does not appear to be out of line with the work of Friedman and Schartz from more than half a century ago.

But, should we buy it? First, there are plenty of things to make us feel uncomfortable about VAR results with regard to monetary policy shocks. As is clear from Ramey's paper, and to anyone who has read the VAR literature closely, results (both qualitative and quantitative) are sensitive to what variables we include in the VAR, and to various other aspects of the setup. Basically, it's not clear we can believe the identifying assumptions. Second, even if take VAR results at face value, the results will only capture the effect of an innovation in monetary policy. But, modern macroeconomics teaches us that this is not what we should actually be interested in. Instead, we should care about the operating characteristics of the economy under alternative well-specified policy rules. These are rules specifying the actions the central bank takes under all possible circumstances. For the Fed, actions would involve setting administered interest rates - principally the interest rate on reserves and the discount rate - and purchasing assets of particular types and maturities.

Once we think generally in terms of policy rules, the notion of long and variable lags goes out the window. In principle, the current state of the economy determines the likelihood of all potential future states of the economy. Then, if we know the central bank's policy rule, we know the the likelihood of all future policy actions. But some of those future economic states of the world may not arise for many years, if ever. For example, if the policy rule is well-specified, it tells us what the central bank will do in the event of another financial crisis. Under what circumstances will the Fed lend to large and troubled financial institutions? How bad does it have to get before the central bank pushes overnight nominal interest rates to zero or lower? To what extent should the central bank engage in quantitative easing? And so on. This is basically what "forward guidance" is about. In a world with forward looking people, promises about future actions matter for economic activity today - monetary policy actions need not precede effects. All of this raises doubts about what we can learn about monetary policy effects from a purely statistical analysis. Unfortunately the data is not very good at speaking for itself.

But, we have models. In those models, we can think about any policy experiments we want (within the bounds of what the model can handle of course), and we can rig those experiments in ways that allow us to think about long and variable lags in a coherent fashion. Basic frictionless models commonly used in macro have essentially no internal propagation. For example, the standard representative agent neoclassical growth model with technology shocks (i.e. RBC) exhibits some propagation through the capital stock - a positive technology shock implies higher investment today, higher capital stock tomorrow, and higher output tomorrow. But that effect is very small, and the basic RBC model fits the persistence in output by applying persistence in the technology shock. Indeed, in that model the properties of the time series of aggregate output are determined primarily by the time series properties of the exogenous technology shock, so that's not much of a theory of propagation. Add monetary elements to basic RBC without other frictions and not much is going to happen. For example, in Cooley and Hansen's cash-in-advance model, monetary impulses don't matter much, and certainly don't produce Friedman's long and variable lags.

Of course, we have frictions. Sticky prices will certainly act to produce nonneutralities of money that will persist. But it's well-known that the quantitative effects are highly sensitive to assumptions about pricing. With Calvo pricing, monetary shocks are a big deal, but with state-dependent pricing, the effects are small. Other work by Francesco Lippi and Fernando Alvarez shows that small changes in the pricing protocol - for example setting two prices (a sale price and a regular price) from which to choose - can dramatically reduce the effect of a money shock. Another propagation mechanism with some claim to support from serious theory is labor search. The fact that successful matches in the labor market take time will act to propagate any shocks in general equilibrium, including monetary shocks. However, there seems to be some debate about how quantitatively important this is.

Probably the best known attempt to quantify the dynamic effects of monetary policy, in an expanded New Keynesian model, is Christiano/Eichenbaum/Evans (CEE). CEE start by first filtering the data through VAR analysis, and then treating the impulse responses in the VAR as data that the model should explain. Thus, a key assumption in the analysis is that the monetary policy shock has been correctly identified in the preliminary VAR step. Given that heroic assumption, what CMM set out to explain are lags in monetary policy that, if not variable, are certainly long:

Output, consumption, and investment [in the VAR impulse responses] respond in a hump-shaped fashion, peaking after about one and a half years and returning to preshock levels after about three years.

So, the responses of real activity to monetary policy shocks estimated by CMM exhibit two key features. First, the effects take a long time to peak and to dissipate, in a manner that seems consistent with the Monetary History and other VAR evidence. Second, the response exhibits delay - that's what the "hump shapes" are about.

So, how do CMM go about fitting this data? Getting the persistence and delay in the effects of monetary policy will require frictions. These are the frictions in the model:

1. Sticky prices: There is Calvo pricing. Not only that, but if a firm gets to re-set its price, it must do that before knowing the current period's monetary shock.
2. Sticky wages: Households set their wages in a Calvo fashion.
3. Sticky utilization: It is costly to change the utilization rate of capital.
4. Cash-in-advance purchases of labor: This works as in Tim Fuerst's segmented markets model of monetary policy, and gives an added kick to employment from a monetary policy shock.
5. Costs of adjustment associated with investment.

What's going on here? For the most part, the five frictions above are not well-grounded in microeconomic theory, nor are they well-supported with microeconomic evidence. We of course know that firms do not make decisions continuously but at discrete points in time. But why should it be costly to adjust the capital stock, or to change capital utilization? It can be infinitely costly for a firm to change its price if the Calvo fairy does not allow it, but in the CMM model it is costless to index price decisions. Why? Because that helps in fitting the data. Ultimately, then, we have a model which does a good job of fitting VAR impulse responses, but seems to have thrown out a lot of economics along the way.

So, what do we know about long and variable lags associated with monetary policy? Not much, it seems. We don't have good theories of persistence and delay associated with monetary policy actions, and it's hard to trust the empirical evidence that is used to argue for long and variable lags. Further, the theory we have tells us that policy design is about evaluating the operating characteristics of economies under alternative policy rules. And, in that context, thinking in terms of actions and lagged responses is wrongheaded. Let's go with that.

I think one can learn a lot by reading FOMC transcripts. But I'm not sure the Romer/Romer measure amounts to much. In particular, I don't like their interpretation of Fed forecasts. It's not clear that we should think of these as capturing the best projection of future macroeconomic variables given current information.

It would be interesting to know if Friedman measured the lags of monetary policy response on past movements in output. In other words , output slumps , monetary policy responds by easing , but output could care less , operating on its own schedule , thus yielding highly variable lags.

In the quote, you can see roughly what Friedman and Schwartz were up to. They looked at turning points in money supply and turning points in what he calls "general business." I haven't read the Monetary History in a long time, but I think "general business" is the NBER "reference cycle," which is roughly an index of aggregate economic activity - not aggregate output, but presumably highly correlated with it. Basically, Friedman and Schwartz showed that money leads aggregate economic activity. It's the informal counterpart of what Sims (1972) is about. Sims showed that money Granger-causes output in the the U.S. time series. Of course Granger causation need not imply economic causation. That was part of Tobin's critique of Friedman and Schwartz. Money could in fact be endogenously responding to output, but appear to lead output in the time series. The endogeneity could come from policy, or from the banking sector, if we're measuring money as M1 or M2, say.

Isn't this almost trivially true in a reserve system? New construction, for example, almost always follows a course of sketch planning, raising capital, detailed planning then building (with some overlap). It seems almost impossible to do it the other way with a CB.

Business cash balances account for a large share of the money stock. It should not be surprising to see firms accumulate cash prior to making purchases (such as investment and employment) nor to seem them run down cash to buffer unexpected declines in sales and/or profits. This is consistent with apparent lags between cash balances and real business activity without implying that firms make investment and employment decisions based on the amount of cash on hand.

That certainly is a good question. It takes a model to beat a model. But at what? We have a lot of different models, and if those models are any good, each one will give us a tiny bit of insight into how the world works. We have a lot of different ideas, manifested in models, about what monetary policy does. I think we're taking things way too seriously if, for example, we take the CEE model and try to literally use that to guide monetary policy. That would surely produce a mess. Similarly, it would be silly to write down a specific rule - some version of the Taylor rule, for example, with provision for financial crises, etc., and commit to it. But, I think it's possible for a committee of individuals, with all their modeling baggage, to make policy decisions in a consistent way, and to speak about those policies, so that, implicitly, the policy rule is well understood.

Exactly. Sometimes economists write down models in an attempt to fit the data, and a lack of fit in the model comes from the fact that decisions appear to be more sluggish in the real world than in the model. So, a cheap way to fix the model is to impose some costs in the model, associated with particular decisions. That's what costly utilization is about. As you point out, there's really not an economically justifiable reason for those costs to be in the model.

Steve, I enjoyed this post, though I’m less pessimistic about CEE (full disclosure: I’m the C in CEE!). I would like to address your five points and then make two observations. 1. Sticky prices are introduced in response to micro evidence on prices and the evidence of monetary non-neutrality. At the same time, I do agree with you that the absence of microfoundations is a huge drawback and out of step with modern economics. So, I look forward to the day when a tractable, microfounded approach is found. 2. I also agree with you that sticky wages are unappealing. However, here the news is better. A microfounded way to capture the observed inertia in wages has been found and sticky wages are no longer necessary (http://faculty.wcas.northwestern.edu/~lchrist/research/alt_offer/ChristianoEichenbaumTrabandt.pdf) . The new approach follows the Diamond-Mortensen-Pissarides vision to labor markets, a vision which I think all of us agree is the best one at this time. 3. Capital utilization plays only a minor role in models and should be dropped. 4. I think `Cash in advance’ got a big boost from the evidence that firms were hurt during the financial crisis when they could not get access to credit to pay for working capital (see http://people.bu.edu/sgilchri/research/GSSZ_inflation.pdf) . 5. The cost of adjustment in investment proposed in CEE has received a lot of support. Matsuyama and Lucca describe interesting ways to microfound it. Eberly, Rebelo and Vincent (JME, 2012) describe micro evidence from COMPUSTAT that support it (ERV provide citations to Matsuyama and Lucca). Another ‘bell and whistle’ that is often mentioned in the context of CEE is habit persistence in consumption. Apart from any introspective evidence on this assumption, there is one generally agreed upon fact that seems hard to understand (without pyrotechnics) unless habit persistence is adopted: that consumption growth appears to rise for a while in the wake of a monetary policy induced fall in the real interest rate. Apart from fitting the data tolerably well (see not only CEE but also Smets and Wouters), the CEE model has also proved to be a useful platform for thinking about financial frictions (see, for example, Gertler and Kiyotaki). For example, the model successfully reconciles the notion that disturances to financial intermediation which hurt investment do no simultaneously trigger a consumption boom (see my 2014 AER paper on this).

Steve. I wrote a reply to your post on my blog. Just dawned on me that Mark Thoma doesn't aggregate my site any more so you might not have noticed it. https://longandvariable.wordpress.com/2015/10/17/steve-williamsons-scepticism-about-empirical-and-saltwater-macro/

Could there be an alternative explanation? I think the key to the long-and-variable puzzle lies in money demand. An argument could be made that monetary policy shocks have instant effect, but it is money demand that creates the lags. In other words, you cannot project the impact of a policy shock unless you know what money demand will do. The issue is that money demand cannot be observed directly due to the ex-post nominal identity between money supply and demand. This casts the illusion that monetary policy is subject to a lag. The good news is that money demand can be deduced from the velocity of money.

What if we model the effects of money supply in a manner consistent with the existence of lags, but then we consider the effect of money demand so that it reflects expectations and mix both effects somewhat ...

I think Larry (he put the C in CEE) is a little too cavalier about sticky prices and wages. There are by now several New Monetarist models that generate the appearance of stickiness in different ways -- and hence are consistent with the broad facts as well as some of the detailed micro data -- but have policy implications dramatically different from Keynesian models. Head et al. in JEEA is one such model focusing on empirical micro issues, but there are various others. Recent work by Tao Zhu generates impulse responses to some kinds of money shocks that display fast rises in output and slow rises in prices, but output does NOT rise because prices are sticky; to the contrary, prices look sticky because output rises. VAR's can be deceiving. I am also working on microfounded models of open market operations and on models of the impact of monetary policy news where prices look stocky to the naive eye, but again policy implications dramatically different from Keynesian models. Finally, Larry's suggestion that the DMP model provides support for sticky wages is off base for several reasons, not the least being that those models have very little to do with money and nominal wages. Why did I post this? LC is clearly one of the world's leading macroeconomists and one of the world's nicest guys. Hence I wanted to try to reduce his confusion ;-)